The present disclosure relates generally to an extremum-seeking control (ESC) system. ESC is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. ESC can be considered a dynamic realization of gradient searching through the use of dither signals. The gradient of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using a negative feedback loop in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system.
Multivariable optimization with non-separable variables can be a difficult problem to solve using ESC because tuning the gains of the feedback loops in each ESC can depend on knowledge of all channels. Previous solutions to this problem use a centralized multivariable extremum-seeking controller that ideally has information about the Hessian of the performance map. However, centralized multivariable controllers are difficult to implement, configure, and troubleshoot, which makes these solutions difficult to adopt in practice.